0580/22 Feb/Mar 2025, Question 17: Recurring Decimals
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 4 marks
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The question, in short
Add the fraction 5/9 to the recurring decimal 0.28 recurring, giving the result as a fraction in simplest form.
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Solution · 4 marks
- 1Let x = 0.2888…, then 100x = 28.888… and 10x = 2.888…
- 290x = 28.888… − 2.888… = 26, so x = 26/90
- 35/9 = 50/90
- 450/90 + 26/90 = 76/90
- 5= 38/45
Answer38/45
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